Solve 3/2-3/frac{9{4}+1}

$$\frac { \frac { 3 } { 2 } - 3 } { \frac { 9 } { 4 } + 1 }$$

Evaluate

$$-\frac{6}{13}\approx -0.461538462$$

Solution Steps

Convert 3 to fraction \frac{6}{2}.

$$\frac{\frac{3}{2}-\frac{6}{2}}{\frac{9}{4}+1}$$

Since \frac{3}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-6}{2}}{\frac{9}{4}+1}$$

Subtract 6 from 3 to get -3.

$$\frac{-\frac{3}{2}}{\frac{9}{4}+1}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{-\frac{3}{2}}{\frac{9}{4}+\frac{4}{4}}$$

Since \frac{9}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{3}{2}}{\frac{9+4}{4}}$$

Add 9 and 4 to get 13.

$$\frac{-\frac{3}{2}}{\frac{13}{4}}$$

Divide -\frac{3}{2} by \frac{13}{4} by multiplying -\frac{3}{2} by the reciprocal of \frac{13}{4}.

$$-\frac{3}{2}\times \frac{4}{13}$$

Multiply -\frac{3}{2} times \frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 4}{2\times 13}$$

Do the multiplications in the fraction \frac{-3\times 4}{2\times 13}.

$$\frac{-12}{26}$$

Reduce the fraction \frac{-12}{26} to lowest terms by extracting and canceling out 2.

$$-\frac{6}{13}$$

Factor

$$-\frac{6}{13} = -0.46153846153846156$$